As far as your title goes, you also don't "feel nausea and vomiting". You "feel nauseous" and you "vomit".
The person in your example "has a headache, feels nauseous and is vomiting". It's slight tautology to say "feels nauseous and is vomiting" though, because "to feel nauseous" means to feel as if you're going to vomit.
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